You have taken the first step by taking your cat to the vet which is right. Now you need to treat your home.
Where ever your cat goes is laden with flea eggs...bedding, upholstry and carpets.
You need to spray your house and get everyone, including the animals out for a few hours.
Spray the baseboards and floors. Put some Vapona strips under your beds and couches; they are thick, yellow and you can cut them up.
Remember that everytime your cat goes outside they are likely to pick up fleas, so you must be vigilant about keeping up their Frontline protection.